it's always worth doing basic checks on something dead, especially as it's usually a power problem. One easy thing to do is to gently remove the power connectors from the mobo, check them over and gently connect them again. Extend this to anything else that looks like it could do with a quick check.
Also try another mains cable, as the fuse could be blown. Do this first.
If it still doesn't work after basic checks, then get your money back. I know it's a PITA, but it can't be helped. It's quite possible that the seller tried scamming you into buying a dud. It's the risk of fraud why I seldom trade on eBay and then only with established businesses with a good reputation.